Accelerated sigmatropic rearrangements of vinylcyclopropanes and vinylcyclobutanes will be developed as powerful new methods for the synthesis of five- and six-membered rings. Electrocyclic reactions and cycloadditions of vinylketenes will be examined as new methods for the synthesis of alicyclic and aromatic compounds. The synthetic utility of these pericyclic reactions will be demonstrated in efficient total syntheses of sesquiterpenes, antibiotic antifungal phenols, and naturally occurring anthracyclines.